Unique Path

来源：互联网发布：急难先锋8016优化编辑：程序博客网时间：2024/06/05 06:10

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

11/1

A very easy problem solved by DP

public class Solution {    public int uniquePaths(int m, int n) {        int[][] grid = new int[m][n];        // note that grid[i][0] = 1 and grid[0][j] = 1        for(int i=0; i<m; i++){            grid[i][0] = 1;        }        for(int j=0; j<n; j++){            grid[0][j] = 1;        }                for(int i=1; i<m; i++){            for(int j=1; j<n; j++){                grid[i][j] = grid[i-1][j] + grid[i][j-1];            }        }                return grid[m-1][n-1];    }}

0 0